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Gimbal lock occurs when using Euler angles to represent 3D rotations, causing a loss of one degree of freedom as two of the rotational axes align. This can lead to unexpected behavior in systems relying on these rotations, such as in animations or aircraft control, necessitating alternative representations like quaternions to avoid the issue.
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Axis-Angle Representation is a mathematical model used to describe the orientation of a rigid body in three-dimensional space, where a rotation is defined by an axis of rotation and an angle of rotation around that axis. This representation is particularly useful in robotics and computer graphics for interpolating rotations and converting between different rotation representations like quaternions and rotation matrices.
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A rotation matrix is a mathematical tool used to perform a rotation in Euclidean space, preserving the object's size and shape while changing its orientation. It is an orthogonal matrix with a determinant of 1, ensuring that the transformation is both linear and reversible.
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Rotation animations make pictures or objects turn around in a circle, like a spinning top. They help make cartoons and video games look more fun and exciting.
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Rotational transformations involve the rotation of objects or coordinate systems around a fixed point or axis, fundamentally altering their orientation in space without changing their shape or size. This concept is pivotal in fields ranging from computer graphics to mechanical engineering, enabling the simulation of physical rotations and the analysis of rotational dynamics.
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